Abstract:We introduce weighted cycles on weaves of general Dynkin types and define a skew-symmetrizable intersection pairing between weighted cycles. We prove that weighted cycles on a weave form a Laurent polynomial algebra and construct a quantization for this algebra using the skew-symmetric intersection pairing in the simply-laced case. We define merodromies along weighted cycles as functions on the decorated flag moduli space of the weave. We relate weighted cycles with cluster variables in a cluster algebra and prove that mutations of weighted cycles are compatible with mutations of cluster variables.
| Comments: | 38 pages, 43 figures |
| Subjects: | Representation Theory (math.RT) |
| MSC classes: | 13F60, 22E46, 05C38, 14M15, 57K31, 81R60 |
| Cite as: | arXiv:2503.08020 [math.RT] |
| (or arXiv:2503.08020v3 [math.RT] for this version) | |
| https://doi.org/10.48550/arXiv.2503.08020 arXiv-issued DOI via DataCite |
From: Daping Weng [view email]
[v1]
Tue, 11 Mar 2025 04:01:21 UTC (50 KB)
[v2]
Wed, 12 Mar 2025 03:39:19 UTC (50 KB)
[v3]
Thu, 21 May 2026 18:52:33 UTC (53 KB)
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